module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 86,
"column": 22
} | {
"line": 89,
"column": 9
} | {
"line": 90,
"column": 2
} | [
{
"pp": "ι : Type u_1\nc : ComplexShape ι\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK : HomologicalComplex C c\ni✝ j✝ : Option ι\ni j : ι\n⊢ (XOpIso K (some i)).hom ≫ (d K (some j) (some i)).op = d K.op (some i) (some j) ≫ (XOpIso K (some j)).hom",
... | [] | by
dsimp [XOpIso]
simp only [d_eq _ rfl rfl, op_comp, assoc, id_comp, comp_id]
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.Embedding.Restriction | {
"line": 38,
"column": 35
} | {
"line": 38,
"column": 65
} | {
"line": 38,
"column": 66
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : ¬c.Rel i j\n⊢ ¬c'.Rel (e.f i) (e.f j)",
"p... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : ¬c.Rel i j\n⊢ ¬c'.Rel (e.f i) (e.f j)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 37
} | {
"line": 54,
"column": 38
} | [
{
"pp": "case left\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni' : ι'\nj : ι\nhj : c'.Rel i' (e.f j)\nhi' : ∀ (i : ι), e.f i ≠ i'\n⊢ c'.Rel (c'.prev (e.f j)) (e.f j)",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"cong... | [
"case left\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ni' : ι'\nj : ι\nhj : c'.Rel i' (e.f j)\nhi' : ∀ (i : ι), e.f i ≠ i'\n⊢ c'.Rel i' (e.f j)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 64,
"column": 15
} | {
"line": 64,
"column": 43
} | {
"line": 64,
"column": 44
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhk : c.Rel j k\na✝ : c'.Rel (c'.prev (e.f k)) (e.f k)\n⊢ c'.Rel (e.f j) (e.f k)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhk : c.Rel j k\na✝ : c'.Rel (c'.prev (e.f k)) (e.f k)\n⊢ c.Rel j k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 43
} | {
"line": 71,
"column": 44
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhj : ¬e.BoundaryGE j\nhjk : ¬c.Rel j (c.next j)\n⊢ ¬e.BoundaryGE (c.next j)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Comple... | [
"case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhj : ¬e.BoundaryGE j\nhjk : ¬c.Rel j (c.next j)\n⊢ ¬e.BoundaryGE j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 76,
"column": 13
} | {
"line": 76,
"column": 34
} | {
"line": 76,
"column": 35
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryGE j\ni' : ι'\nhi' : c'.Rel i' (e.f j)\na : ι\nha : e.f a = i'\n⊢ c'.Rel (e.f a) (e.f j)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryGE j\ni' : ι'\nhi' : c'.Rel i' (e.f j)\na : ι\nha : e.f a = i'\n⊢ c'.Rel i' (e.f j)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 82,
"column": 26
} | {
"line": 82,
"column": 54
} | {
"line": 82,
"column": 55
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : c.Rel i j\n⊢ c'.Rel (e.f i) (e.f j)",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : c.Rel i j\n⊢ c.Rel i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Extend | {
"line": 237,
"column": 2
} | {
"line": 237,
"column": 13
} | {
"line": 237,
"column": 14
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK : HomologicalComplex C c\ne : c.Embedding c'\ni✝ : ι'\n⊢ (extendMap (𝟙 K) e).f i✝ = (𝟙 (K.extend e)).f i✝",
"ppTerm": "?m.45... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : HasZeroObject C\ninst✝ : HasZeroMorphisms C\nK : HomologicalComplex C c\ne : c.Embedding c'\ni✝ : ι'\n⊢ (extendMap (𝟙 K) e).f i✝ = 𝟙 ((K.extend e).X i✝)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 84,
"column": 39
} | {
"line": 84,
"column": 61
} | {
"line": 84,
"column": 62
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : ¬c.Rel i j\n⊢ ¬c.Rel (c.prev j) j",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrAr... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : ¬c.Rel i j\n⊢ ¬c.Rel i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 84,
"column": 6
} | {
"line": 84,
"column": 74
} | {
"line": 84,
"column": 75
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : ¬c.Rel i j\n⊢ j = i",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhij : c.prev j = i\nhj : ¬e.BoundaryGE j\nhij' : ¬c.Rel i j\n⊢ j = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 91,
"column": 19
} | {
"line": 91,
"column": 41
} | {
"line": 91,
"column": 42
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhij' : ¬c.Rel j j\nhj' : c'.Rel (c'.prev (e.f j)) (e.f j)\nhj : c'.Rel (c'.prev (e.f j)) (e.f j) → ∃ x, c'.Rel (e.f x) (e.f j)\ni : ι\nhij : i = j\nhi : c.Rel i j\n⊢ c.Rel j j",
"pp... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhij' : ¬c.Rel j j\nhj' : c'.Rel (c'.prev (e.f j)) (e.f j)\nhj : c'.Rel (c'.prev (e.f j)) (e.f j) → ∃ x, c'.Rel (e.f x) (e.f j)\ni : ι\nhij : i = j\nhi : c.Rel i j\n⊢ c.Rel j j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 96,
"column": 19
} | {
"line": 96,
"column": 40
} | {
"line": 96,
"column": 41
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryGE j\ninst✝ : e.IsTruncLE\ni : ι\nhi : e.f i = c'.prev (e.f j)\n⊢ c'.Rel (e.f i) (e.f j)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryGE j\ninst✝ : e.IsTruncLE\ni : ι\nhi : e.f i = c'.prev (e.f j)\n⊢ c'.Rel (c'.prev (e.f j)) (e.f j)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 37
} | {
"line": 107,
"column": 38
} | [
{
"pp": "case left\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nk' : ι'\nj : ι\nhj : c'.Rel (e.f j) k'\nhk' : ∀ (i : ι), e.f i ≠ k'\n⊢ c'.Rel (e.f j) (c'.next (e.f j))",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"cong... | [
"case left\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nk' : ι'\nj : ι\nhj : c'.Rel (e.f j) k'\nhk' : ∀ (i : ι), e.f i ≠ k'\n⊢ c'.Rel (e.f j) k'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 117,
"column": 15
} | {
"line": 117,
"column": 43
} | {
"line": 117,
"column": 44
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhi : c.Rel i j\na✝ : c'.Rel (e.f i) (c'.next (e.f i))\n⊢ c'.Rel (e.f i) (e.f j)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\ni j : ι\nhi : c.Rel i j\na✝ : c'.Rel (e.f i) (c'.next (e.f i))\n⊢ c.Rel i j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 43
} | {
"line": 124,
"column": 44
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhj : ¬e.BoundaryLE j\nhij : ¬c.Rel (c.prev j) j\n⊢ ¬e.BoundaryLE (c.prev j)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrA... | [
"case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhj : ¬e.BoundaryLE j\nhij : ¬c.Rel (c.prev j) j\n⊢ ¬e.BoundaryLE j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 129,
"column": 13
} | {
"line": 129,
"column": 34
} | {
"line": 129,
"column": 35
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryLE j\nk' : ι'\nhk' : c'.Rel (e.f j) k'\na : ι\nha : e.f a = k'\n⊢ c'.Rel (e.f j) (e.f a)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryLE j\nk' : ι'\nhk' : c'.Rel (e.f j) k'\na : ι\nha : e.f a = k'\n⊢ c'.Rel (e.f j) k'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 135,
"column": 26
} | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 55
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : c.Rel j k\n⊢ c'.Rel (e.f j) (e.f k)",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : c.Rel j k\n⊢ c.Rel j k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 137,
"column": 39
} | {
"line": 137,
"column": 61
} | {
"line": 137,
"column": 62
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : ¬c.Rel j k\n⊢ ¬c.Rel j (c.next j)",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrAr... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : ¬c.Rel j k\n⊢ ¬c.Rel j k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 137,
"column": 6
} | {
"line": 137,
"column": 74
} | {
"line": 137,
"column": 75
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : ¬c.Rel j k\n⊢ j = k",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj k : ι\nhjk : c.next j = k\nhj : ¬e.BoundaryLE j\nhjk' : ¬c.Rel j k\n⊢ j = k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 144,
"column": 19
} | {
"line": 144,
"column": 41
} | {
"line": 144,
"column": 42
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhjk' : ¬c.Rel j j\nhj' : c'.Rel (e.f j) (c'.next (e.f j))\nhj : c'.Rel (e.f j) (c'.next (e.f j)) → ∃ x, c'.Rel (e.f j) (e.f x)\nk : ι\nhjk : k = j\nhk : c.Rel j k\n⊢ c.Rel j j",
"pp... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsRelIff\nj : ι\nhjk' : ¬c.Rel j j\nhj' : c'.Rel (e.f j) (c'.next (e.f j))\nhj : c'.Rel (e.f j) (c'.next (e.f j)) → ∃ x, c'.Rel (e.f j) (e.f x)\nk : ι\nhjk : k = j\nhk : c.Rel j k\n⊢ c.Rel j j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 38
} | {
"line": 155,
"column": 39
} | [
{
"pp": "case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsTruncGE\nj k : ι\nhjk : c.next j = k\nhj : ¬c'.Rel (e.f j) (c'.next (e.f j))\nhj' : c'.Rel (e.f j) (e.f (c.next j))\n⊢ c'.Rel (e.f j) (c'.next (e.f j))",
"ppTerm": "?neg✝",
"assigned... | [
"case neg\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\ninst✝ : e.IsTruncGE\nj k : ι\nhjk : c.next j = k\nhj : ¬c'.Rel (e.f j) (c'.next (e.f j))\nhj' : c'.Rel (e.f j) (e.f (c.next j))\n⊢ c'.Rel (e.f j) (e.f (c.next j))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.Boundary | {
"line": 163,
"column": 19
} | {
"line": 163,
"column": 40
} | {
"line": 163,
"column": 41
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryLE j\ninst✝ : e.IsTruncGE\nk : ι\nhk : e.f k = c'.next (e.f j)\n⊢ c'.Rel (e.f j) (e.f k)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nj : ι\nhj : e.BoundaryLE j\ninst✝ : e.IsTruncGE\nk : ι\nhk : e.f k = c'.next (e.f j)\n⊢ c'.Rel (e.f j) (c'.next (e.f j))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.HomEquiv | {
"line": 85,
"column": 42
} | {
"line": 85,
"column": 53
} | {
"line": 85,
"column": 54
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.Ha... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.HasLift φ\ni' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.HomEquiv | {
"line": 87,
"column": 42
} | {
"line": 87,
"column": 53
} | {
"line": 87,
"column": 54
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.Ha... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.HasLift φ\ni' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.HomEquiv | {
"line": 94,
"column": 14
} | {
"line": 94,
"column": 25
} | {
"line": 94,
"column": 26
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.Ha... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.HasLift φ\ni' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.HomEquiv | {
"line": 96,
"column": 44
} | {
"line": 96,
"column": 55
} | {
"line": 96,
"column": 56
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.Ha... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nφ : K.restriction e ⟶ L\nhφ : e.HasLift φ\ni' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.HomEquiv | {
"line": 190,
"column": 38
} | {
"line": 190,
"column": 49
} | {
"line": 190,
"column": 50
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nψ : K ⟶ L.extend e\ni' : ι'\nhi' :... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\ne : c.Embedding c'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nK : HomologicalComplex C c'\nL : HomologicalComplex C c\ninst✝ : e.IsRelIff\nψ : K ⟶ L.extend e\ni' : ι'\nhi' : ¬∃ i, e.f i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 84
} | {
"line": 222,
"column": 4
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝³ : Category.{v, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nX₁✝ X₂✝ X₃✝ : CochainComplex C ℤ\nf : X₁✝ ⟶ X₂✝\ng : X₂✝ ⟶ X₃✝\ninst✝ : HasZeroObject C\nX₁ X₂ X₃ : CochainComplex C ℤ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nα : mappingCone.triangle u₁₂ ⟶ mapping... | [] | exact ((quotient _ _).mapTriangle.map α).comm₃.symm.trans (by dsimp [α]; simp) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 84
} | {
"line": 222,
"column": 4
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝³ : Category.{v, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nX₁✝ X₂✝ X₃✝ : CochainComplex C ℤ\nf : X₁✝ ⟶ X₂✝\ng : X₂✝ ⟶ X₃✝\ninst✝ : HasZeroObject C\nX₁ X₂ X₃ : CochainComplex C ℤ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nα : mappingCone.triangle u₁₂ ⟶ mapping... | [] | exact ((quotient _ _).mapTriangle.map α).comm₃.symm.trans (by dsimp [α]; simp) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.HomotopyCategory.Triangulated | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 84
} | {
"line": 222,
"column": 4
} | [
{
"pp": "case refine_2\nC : Type u_1\ninst✝³ : Category.{v, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasBinaryBiproducts C\nX₁✝ X₂✝ X₃✝ : CochainComplex C ℤ\nf : X₁✝ ⟶ X₂✝\ng : X₂✝ ⟶ X₃✝\ninst✝ : HasZeroObject C\nX₁ X₂ X₃ : CochainComplex C ℤ\nu₁₂ : X₁ ⟶ X₂\nu₂₃ : X₂ ⟶ X₃\nα : mappingCone.triangle u₁₂ ⟶ mapping... | [] | exact ((quotient _ _).mapTriangle.map α).comm₃.symm.trans (by dsimp [α]; simp) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 87,
"column": 38
} | {
"line": 87,
"column": 60
} | {
"line": 87,
"column": 61
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : ∀ (i' : ι'), L.HasHomolog... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : ∀ (i' : ι'), L.HasHomology i'\ni j k ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 197,
"column": 52
} | {
"line": 201,
"column": 38
} | {
"line": 203,
"column": 0
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝³ : Category.{v_1, u_3} C\ninst✝² : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝¹ : e.IsTruncGE\ninst✝ : ∀ (i' : ι'), K.HasHomology i'\n⊢ truncGE'Map (𝟙 K) e = 𝟙 (K.truncGE' e)",
... | [] | by
ext i
by_cases hi : e.BoundaryGE i
· simp [truncGE'Map_f_eq_opcyclesMap _ _ hi rfl]
· simp [truncGE'Map_f_eq _ _ hi rfl] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 98,
"column": 23
} | {
"line": 98,
"column": 58
} | {
"line": 98,
"column": 59
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : ∀ (i' : ι'), L.HasHomolog... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : ∀ (i' : ι'), L.HasHomology i'\ni j k ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 151,
"column": 40
} | {
"line": 151,
"column": 63
} | {
"line": 152,
"column": 4
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomolo... | [] | rw [← hj', e.next_f hk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 159,
"column": 58
} | {
"line": 159,
"column": 79
} | {
"line": 159,
"column": 80
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomolo... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomology i'\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 186,
"column": 52
} | {
"line": 186,
"column": 63
} | {
"line": 186,
"column": 64
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nj : ι\nj' : ι'\nhj' :... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nj : ι\nj' : ι'\nhj' : e.f j = j'\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncLEHomology | {
"line": 135,
"column": 10
} | {
"line": 135,
"column": 21
} | {
"line": 135,
"column": 22
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : Abelian C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝ : e.IsTruncLE\ni' j' : ι'\nhij' : c'.Rel i' j'\nhj : ¬∃ j, e.f j = j'\n⊢ ∀ (i : ι), e.f i ≠ j'",
"ppTerm": ... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : Abelian C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝ : e.IsTruncLE\ni' j' : ι'\nhij' : c'.Rel i' j'\nhj : ¬∃ j, e.f j = j'\n⊢ ∀ (i : ι), ¬e.f i = j'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 193,
"column": 47
} | {
"line": 193,
"column": 71
} | {
"line": 193,
"column": 72
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nj : ι\nj' : ι'\nhj' :... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nj : ι\nj' : ι'\nhj' : e.f j = j'\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncLEHomology | {
"line": 142,
"column": 52
} | {
"line": 142,
"column": 63
} | {
"line": 142,
"column": 64
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : Abelian C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝ : e.IsTruncLE\ni' : ι'\nhi' : ¬∃ j', c'.Rel i' j'\n⊢ ∀ (j : ι'), ¬c'.Rel i' j",
"ppTerm": "?m.87",
"ass... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝² : Category.{v_1, u_3} C\ninst✝¹ : Abelian C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝ : e.IsTruncLE\ni' : ι'\nhi' : ¬∃ j', c'.Rel i' j'\n⊢ ∀ (j : ι'), ¬c'.Rel i' j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 329,
"column": 30
} | {
"line": 329,
"column": 51
} | {
"line": 329,
"column": 52
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'), L.HasHomo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 214,
"column": 56
} | {
"line": 214,
"column": 67
} | {
"line": 214,
"column": 68
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\na✝ : K.IsSupported e\... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\na✝ : K.IsSupported e\ni' : ι'\nhi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 214,
"column": 56
} | {
"line": 214,
"column": 67
} | {
"line": 214,
"column": 68
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\na✝ : K.IsSupported e\... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\na✝ : K.IsSupported e\ni' : ι'\nhi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 350,
"column": 37
} | {
"line": 350,
"column": 48
} | {
"line": 350,
"column": 49
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁶ : Category.{v_1, u_3} C\ninst✝⁵ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁴ : e.IsTruncGE\ninst✝³ : ∀ (i' : ι'), K.HasHomology i'\ninst✝² : ∀ (i' : ι'), L.HasHomo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 220,
"column": 22
} | {
"line": 220,
"column": 81
} | {
"line": 220,
"column": 82
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : (K.truncGE e).Ac... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : (K.truncGE e).Acyclic\ni : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 224,
"column": 6
} | {
"line": 224,
"column": 67
} | {
"line": 224,
"column": 68
} | [
{
"pp": "case pos\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : K.IsSu... | [
"case pos\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : K.IsSupportedOutsi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 225,
"column": 46
} | {
"line": 225,
"column": 57
} | {
"line": 225,
"column": 58
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : K.IsSupportedOut... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\nK : HomologicalComplex C c'\ne : c.Embedding c'\ninst✝² : e.IsTruncGE\ninst✝¹ : ∀ (i' : ι'), K.HasHomology i'\ninst✝ : HasZeroObject C\nhK : K.IsSupportedOutside e\ni' :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 78,
"column": 6
} | {
"line": 79,
"column": 9
} | {
"line": 80,
"column": 4
} | [
{
"pp": "case left.inl.inl\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\nac : e₁.AreComplementary e₂\ni₁ j₁ : ι₁\nh : fromSum e₁ e₂ (Sum.inl i₁) = fromSum e₁ e₂ (Sum.inl j₁)\n⊢ Sum.inl i₁ = Sum.inl j₁",
... | [] | obtain rfl := e₁.injective_f h
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 78,
"column": 6
} | {
"line": 79,
"column": 9
} | {
"line": 80,
"column": 4
} | [
{
"pp": "case left.inl.inl\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\nac : e₁.AreComplementary e₂\ni₁ j₁ : ι₁\nh : fromSum e₁ e₂ (Sum.inl i₁) = fromSum e₁ e₂ (Sum.inl j₁)\n⊢ Sum.inl i₁ = Sum.inl j₁",
... | [] | obtain rfl := e₁.injective_f h
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Homology.Embedding.ExtendHomology | {
"line": 446,
"column": 39
} | {
"line": 446,
"column": 50
} | {
"line": 446,
"column": 51
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L : HomologicalComplex C c\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝¹ : ∀ (j : ι), K.HasHomology j\ninst✝ : ∀ (j : ι), L.HasHomology ... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L : HomologicalComplex C c\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝¹ : ∀ (j : ι), K.HasHomology j\ninst✝ : ∀ (j : ι), L.HasHomology j\nh : ∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 244,
"column": 4
} | {
"line": 244,
"column": 37
} | {
"line": 244,
"column": 38
} | [
{
"pp": "case mp\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.... | [
"case mp\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomology ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGE | {
"line": 384,
"column": 66
} | {
"line": 384,
"column": 77
} | {
"line": 384,
"column": 78
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁷ : Category.{v_1, u_3} C\ninst✝⁶ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁵ : e.IsTruncGE\ninst✝⁴ : ∀ (i' : ι'), K.HasHomology i'\ninst✝³ : ∀ (i' : ι'... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁷ : Category.{v_1, u_3} C\ninst✝⁶ : HasZeroMorphisms C\nK L M : HomologicalComplex C c'\nφ : K ⟶ L\nφ' : L ⟶ M\ne : c.Embedding c'\ninst✝⁵ : e.IsTruncGE\ninst✝⁴ : ∀ (i' : ι'), K.HasHomology i'\ninst✝³ : ∀ (i' : ι'), L.HasHomo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.ExtendHomology | {
"line": 446,
"column": 39
} | {
"line": 446,
"column": 50
} | {
"line": 446,
"column": 51
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L : HomologicalComplex C c\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝¹ : ∀ (j : ι), K.HasHomology j\ninst✝ : ∀ (j : ι), L.HasHomology ... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁴ : Category.{v_1, u_3} C\ninst✝³ : HasZeroMorphisms C\ninst✝² : HasZeroObject C\nK L : HomologicalComplex C c\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝¹ : ∀ (j : ι), K.HasHomology j\ninst✝ : ∀ (j : ι), L.HasHomology j\nh : ∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 248,
"column": 6
} | {
"line": 248,
"column": 37
} | {
"line": 248,
"column": 38
} | [
{
"pp": "case pos\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L... | [
"case pos\nι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomology... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 250,
"column": 56
} | {
"line": 250,
"column": 67
} | {
"line": 250,
"column": 68
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomolo... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomology i'\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.TruncGEHomology | {
"line": 250,
"column": 56
} | {
"line": 250,
"column": 67
} | {
"line": 250,
"column": 68
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomolo... | [
"ι : Type u_1\nι' : Type u_2\nc : ComplexShape ι\nc' : ComplexShape ι'\nC : Type u_3\ninst✝⁵ : Category.{v_1, u_3} C\ninst✝⁴ : HasZeroMorphisms C\nK L : HomologicalComplex C c'\nφ : K ⟶ L\ne : c.Embedding c'\ninst✝³ : e.IsTruncGE\ninst✝² : ∀ (i' : ι'), K.HasHomology i'\ninst✝¹ : ∀ (i' : ι'), L.HasHomology i'\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.AreComplementary | {
"line": 323,
"column": 6
} | {
"line": 323,
"column": 54
} | {
"line": 323,
"column": 55
} | [
{
"pp": "case inl\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\nC : Type u_4\ninst✝³ : Category.{v_1, u_4} C\ninst✝² : Abelian C\nK : HomologicalComplex C c\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\ninst✝¹ : e₁.IsTruncLE\ninst✝ : e₂.IsTruncGE\nac :... | [
"case inl\nι : Type u_1\nι₁ : Type u_2\nι₂ : Type u_3\nc : ComplexShape ι\nc₁ : ComplexShape ι₁\nc₂ : ComplexShape ι₂\nC : Type u_4\ninst✝³ : Category.{v_1, u_4} C\ninst✝² : Abelian C\nK : HomologicalComplex C c\ne₁ : c₁.Embedding c\ne₂ : c₂.Embedding c\ninst✝¹ : e₁.IsTruncLE\ninst✝ : e₂.IsTruncGE\nac : e₁.AreCompl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 114,
"column": 8
} | {
"line": 114,
"column": 60
} | {
"line": 114,
"column": 61
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : i < n\ninst✝ : K.IsStrictlyGE n\n⊢ ∀ (i_1 : ℕ), (embeddingUpIntGE n).f i_1 ≠ i",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instOne",
... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : i < n\ninst✝ : K.IsStrictlyGE n\n⊢ i < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 119,
"column": 8
} | {
"line": 119,
"column": 60
} | {
"line": 119,
"column": 61
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : n < i\ninst✝ : K.IsStrictlyLE n\n⊢ ∀ (i_1 : ℕ), (embeddingUpIntLE n).f i_1 ≠ i",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ComplexShape.embed... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : n < i\ninst✝ : K.IsStrictlyLE n\n⊢ n < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 124,
"column": 8
} | {
"line": 124,
"column": 60
} | {
"line": 124,
"column": 61
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : i < n\ninst✝ : K.IsGE n\n⊢ ∀ (i_1 : ℕ), (embeddingUpIntGE n).f i_1 ≠ i",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instOne",
"AddGr... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : i < n\ninst✝ : K.IsGE n\n⊢ i < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Embedding.CochainComplex | {
"line": 129,
"column": 8
} | {
"line": 129,
"column": 60
} | {
"line": 129,
"column": 61
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : n < i\ninst✝ : K.IsLE n\n⊢ ∀ (i_1 : ℕ), (embeddingUpIntLE n).f i_1 ≠ i",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ComplexShape.embeddingUpIn... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : HasZeroMorphisms C\nK : CochainComplex C ℤ\nn i : ℤ\nhi : n < i\ninst✝ : K.IsLE n\n⊢ n < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.SingleHomology | {
"line": 40,
"column": 2
} | {
"line": 41,
"column": 9
} | {
"line": 41,
"column": 10
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nι : Type u_1\ninst✝ : DecidableEq ι\nc : ComplexShape ι\nj : ι\nA : C\ni : ι\nhi : i ≠ j\n⊢ IsZero (((single C c j).obj A).homology i)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : HasZeroMorphisms C\ninst✝¹ : HasZeroObject C\nι : Type u_1\ninst✝ : DecidableEq ι\nc : ComplexShape ι\nj : ι\nA : C\ni : ι\nhi : i ≠ j\n⊢ ((single C c j).obj A).ExactAt i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.HomEquiv | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 13
} | {
"line": 65,
"column": 14
} | [
{
"pp": "C₁ : Type u_2\nC₂ : Type u_3\nD₁ : Type u_5\nD₂ : Type u_6\ninst✝⁵ : Category.{v_2, u_2} C₁\ninst✝⁴ : Category.{v_3, u_3} C₂\ninst✝³ : Category.{v_5, u_5} D₁\ninst✝² : Category.{v_6, u_6} D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nL₁ : C₁ ⥤ D₁\ninst✝¹ : L₁.IsLo... | [
"C₁ : Type u_2\nC₂ : Type u_3\nD₁ : Type u_5\nD₂ : Type u_6\ninst✝⁵ : Category.{v_2, u_2} C₁\ninst✝⁴ : Category.{v_3, u_3} C₂\ninst✝³ : Category.{v_5, u_5} D₁\ninst✝² : Category.{v_6, u_6} D₂\nW₁ : MorphismProperty C₁\nW₂ : MorphismProperty C₂\nΦ : LocalizerMorphism W₁ W₂\nL₁ : C₁ ⥤ D₁\ninst✝¹ : L₁.IsLocalization W... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Localization.HomEquiv | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 13
} | {
"line": 91,
"column": 14
} | [
{
"pp": "C₁ : Type u_2\nD₁ : Type u_5\ninst✝² : Category.{v_2, u_2} C₁\ninst✝¹ : Category.{v_5, u_5} D₁\nW₁ : MorphismProperty C₁\nL₁ : C₁ ⥤ D₁\ninst✝ : L₁.IsLocalization W₁\nX Y : C₁\nf : L₁.obj X ⟶ L₁.obj Y\n⊢ (id W₁).homMap L₁ L₁ f = f",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
... | [
"C₁ : Type u_2\nD₁ : Type u_5\ninst✝² : Category.{v_2, u_2} C₁\ninst✝¹ : Category.{v_5, u_5} D₁\nW₁ : MorphismProperty C₁\nL₁ : C₁ ⥤ D₁\ninst✝ : L₁.IsLocalization W₁\nX Y : C₁\nf : L₁.obj X ⟶ L₁.obj Y\n⊢ (id W₁).homMap L₁ L₁ f = f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomologySequenceLemmas | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 15
} | {
"line": 133,
"column": 16
} | [
{
"pp": "case neg\nC : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS₁ S₂ : ShortComplex (HomologicalComplex C c)\nφ : S₁ ⟶ S₂\nhS₁ : S₁.ShortExact\nhS₂ : S₂.ShortExact\ni : ι\nh₁ : Epi (homologyMap φ.τ₁ i)\nh₂ : Mono (homologyMap φ.τ₂ i)\nh₃ : ∀ (j : ι), c.Rel ... | [
"case neg\nC : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS₁ S₂ : ShortComplex (HomologicalComplex C c)\nφ : S₁ ⟶ S₂\nhS₁ : S₁.ShortExact\nhS₂ : S₂.ShortExact\ni : ι\nh₁ : Epi (homologyMap φ.τ₁ i)\nh₂ : Mono (homologyMap φ.τ₂ i)\nh₃ : ∀ (j : ι), c.Rel i j → Mono (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomologySequenceLemmas | {
"line": 154,
"column": 57
} | {
"line": 154,
"column": 68
} | {
"line": 154,
"column": 69
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS₁ S₂ : ShortComplex (HomologicalComplex C c)\nφ : S₁ ⟶ S₂\nhS₁ : S₁.ShortExact\nhS₂ : S₂.ShortExact\ni : ι\nh₁ : Epi (homologyMap φ.τ₂ i)\nh₂ : ∀ (j : ι), c.Rel i j → Epi (homologyMap φ.τ₁ j)\nh₃ : ∀ (j ... | [
"C : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nS₁ S₂ : ShortComplex (HomologicalComplex C c)\nφ : S₁ ⟶ S₂\nhS₁ : S₁.ShortExact\nhS₂ : S₂.ShortExact\ni : ι\nh₁ : Epi (homologyMap φ.τ₂ i)\nh₂ : ∀ (j : ι), c.Rel i j → Epi (homologyMap φ.τ₁ j)\nh₃ : ∀ (j : ι), c.Rel ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.Refinements | {
"line": 77,
"column": 85
} | {
"line": 79,
"column": 61
} | {
"line": 81,
"column": 0
} | [
{
"pp": "C : Type u_1\nι : Type u_2\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nc : ComplexShape ι\nK : HomologicalComplex C c\nA : C\ni : ι\nz : A ⟶ K.X i\nj : ι\nhj : c.prev i = j\n⊢ z ≫ K.pOpcycles i = 0 ↔ ∃ A' π, ∃ (_ : Epi π), ∃ x, π ≫ z = x ≫ K.d j i",
"ppTerm": "?m.66",
"assigned": true,
... | [] | by
subst hj
apply (K.sc i).comp_pOpcycles_eq_zero_iff_up_to_refinements | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 111,
"column": 22
} | {
"line": 111,
"column": 33
} | {
"line": 111,
"column": 34
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Abelian C\ninst✝¹ : HasExt C\nX Y : C\na b : ℤ\ninst✝ : HasDerivedCategory C\nthis :\n ∀ (a b : ℤ),\n Small.{w, w'}\n ((shiftFunctor (DerivedCategory C) a).obj ((singleFunctor C 0).obj X) ⟶\n (shiftFunctor (DerivedCategory C) b).obj ((sin... | [
"C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Abelian C\ninst✝¹ : HasExt C\nX Y : C\na b : ℤ\ninst✝ : HasDerivedCategory C\nthis :\n ∀ (a b : ℤ),\n Small.{w, w'}\n ((shiftFunctor (DerivedCategory C) a).obj ((singleFunctor C 0).obj X) ⟶\n (shiftFunctor (DerivedCategory C) b).obj ((singleFunctor C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.ShortExact | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 55
} | {
"line": 76,
"column": 4
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex (CochainComplex C ℤ)\nf : S₁ ⟶ S₂\ni : ℤ\n⊢ (map S₁.f S₂.f f.τ₁ f.τ₂ ⋯ ≫ descShortComplex S₂).f i = (descShortComplex S₁ ≫ f.τ₃).f i",
"ppTerm": "?m.90",
"assigned": true,
"usedConstants": [
"Categor... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex (CochainComplex C ℤ)\nf : S₁ ⟶ S₂\ni : ℤ\n⊢ f.τ₂.f i ≫ S₂.g.f i = S₁.g.f i ≫ f.τ₃.f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.HomotopyCategory.ShortExact | {
"line": 98,
"column": 73
} | {
"line": 98,
"column": 84
} | {
"line": 98,
"column": 85
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex (CochainComplex C ℤ)\nhS : S.ShortExact\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nA : C\nx : A ⟶ (HomologicalComplex.homologyFunctor C (up ℤ) n₀).obj (mappingCone S.f)\n⊢ (up ℤ).next n₀ = n₁",
"ppTerm": "?m.296",
"assigned": t... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex (CochainComplex C ℤ)\nhS : S.ShortExact\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nA : C\nx : A ⟶ (HomologicalComplex.homologyFunctor C (up ℤ) n₀).obj (mappingCone S.f)\n⊢ n₀ + 1 = n₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | {
"line": 93,
"column": 8
} | {
"line": 93,
"column": 45
} | {
"line": 93,
"column": 46
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 3\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_13)\nh₁ : Mono (app' φ 1 mono_of_epi_of_mono_of_mono'._proof_11)\nh₃ : Mono (app' φ 3 mono_of_epi_of_mono_of... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 3\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_13)\nh₁ : Mono (app' φ 1 mono_of_epi_of_mono_of_mono'._proof_11)\nh₃ : Mono (app' φ 3 mono_of_epi_of_mono_of_mono'._proo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 61
} | {
"line": 338,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nf : X ⟶ Y\n⊢ mk₀ (-f) = -mk₀ f",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShiftedHom.mk₀.congr_simp",
"NegZeroClass... | [] | letI := HasDerivedCategory.standard C; ext; simp [neg_hom'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 61
} | {
"line": 338,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nX Y : C\nf : X ⟶ Y\n⊢ mk₀ (-f) = -mk₀ f",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShiftedHom.mk₀.congr_simp",
"NegZeroClass... | [] | letI := HasDerivedCategory.standard C; ext; simp [neg_hom'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | {
"line": 130,
"column": 8
} | {
"line": 130,
"column": 45
} | {
"line": 130,
"column": 46
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 3\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_13)\nh₂ : Epi (app' φ 2 mono_of_epi_of_mono_of_mono'._proof_4)\nh₃ : Mono (app' φ 3 mono_of_epi_of_mono_of_m... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 3\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_13)\nh₂ : Epi (app' φ 2 mono_of_epi_of_mono_of_mono'._proof_4)\nh₃ : Mono (app' φ 3 mono_of_epi_of_mono_of_mono'._proof_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | {
"line": 229,
"column": 2
} | {
"line": 231,
"column": 13
} | {
"line": 232,
"column": 2
} | [
{
"pp": "case refine_1\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.map' 0 2 mono_of_epi_of_mono_of_mono'._proof_2 mono_of_epi_of_epi_mono'._proof_1 = 0\nhR₁' : Epi (R₁.map' 1 2 mono_of_epi_of_mono_of_mono'._proof_6 mono_of_epi_of_epi_mono... | [
"case refine_2\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.map' 0 2 mono_of_epi_of_mono_of_mono'._proof_2 mono_of_epi_of_epi_mono'._proof_1 = 0\nhR₁' : Epi (R₁.map' 1 2 mono_of_epi_of_mono_of_mono'._proof_6 mono_of_epi_of_epi_mono'._proof_1)\... | · dsimp
rw [← Functor.map_comp]
exact hR₁ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Homology.HomotopyCategory.ShortExact | {
"line": 119,
"column": 24
} | {
"line": 119,
"column": 35
} | {
"line": 119,
"column": 36
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex (CochainComplex C ℤ)\nhS : S.ShortExact\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nA : C\nx : A ⟶ (HomologicalComplex.homologyFunctor C (up ℤ) n₀).obj (mappingCone S.f)\nA' : C\nπ : A' ⟶ A\nw✝¹ : Epi π\nx' : A' ⟶ (mappingCone S.f).X n₀... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex (CochainComplex C ℤ)\nhS : S.ShortExact\nn₀ n₁ : ℤ\nh : n₀ + 1 = n₁\nA : C\nx : A ⟶ (HomologicalComplex.homologyFunctor C (up ℤ) n₀).obj (mappingCone S.f)\nA' : C\nπ : A' ⟶ A\nw✝¹ : Epi π\nx' : A' ⟶ (mappingCone S.f).X n₀\nw✝ : x' ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | {
"line": 238,
"column": 33
} | {
"line": 238,
"column": 70
} | {
"line": 238,
"column": 71
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nhR₁' : Epi (R₁.map' 1 2 mono_of_epi_of_mono_of_mono'._proof_6 mono_of_epi_of_epi_mono'._proof_1)\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_2)\nh₁ : M... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nhR₁' : Epi (R₁.map' 1 2 mono_of_epi_of_mono_of_mono'._proof_6 mono_of_epi_of_epi_mono'._proof_1)\nh₀ : Epi (app' φ 0 mono_of_epi_of_mono_of_mono'._proof_2)\nh₁ : Mono (app' φ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.DiagramLemmas.Four | {
"line": 261,
"column": 8
} | {
"line": 261,
"column": 45
} | {
"line": 261,
"column": 46
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nhR₂' : Mono (R₂.map' 0 1 mono_of_epi_of_mono_of_mono'._proof_9 mono_of_epi_of_mono_of_mono'._proof_6)\nh₀ : Epi (app' φ 1 mono_of_epi_of_mono_of_mono'._proof_6)\nh... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nR₁ R₂ : ComposableArrows C 2\nφ : R₁ ⟶ R₂\nhR₁ : R₁.Exact\nhR₂ : R₂.Exact\nhR₂' : Mono (R₂.map' 0 1 mono_of_epi_of_mono_of_mono'._proof_9 mono_of_epi_of_mono_of_mono'._proof_6)\nh₀ : Epi (app' φ 1 mono_of_epi_of_mono_of_mono'._proof_6)\nh₁ : Mono (ap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Triangulated.Opposite.Basic | {
"line": 93,
"column": 2
} | {
"line": 95,
"column": 32
} | {
"line": 97,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasShift C ℤ\nX : Cᵒᵖ\n⊢ (shiftFunctorZero Cᵒᵖ ℤ).inv.app X =\n ((shiftFunctorZero C ℤ).hom.app (Opposite.unop X)).op ≫ (shiftFunctorOpIso C 0 0 ⋯).inv.app X",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"CategoryThe... | [] | rw [← cancel_epi ((shiftFunctorZero Cᵒᵖ ℤ).hom.app X), Iso.hom_inv_id_app,
shiftFunctorZero_op_hom_app, assoc, ← op_comp_assoc, Iso.hom_inv_id_app, op_id,
id_comp, Iso.hom_inv_id_app] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Triangulated.Opposite.Basic | {
"line": 93,
"column": 2
} | {
"line": 95,
"column": 32
} | {
"line": 97,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasShift C ℤ\nX : Cᵒᵖ\n⊢ (shiftFunctorZero Cᵒᵖ ℤ).inv.app X =\n ((shiftFunctorZero C ℤ).hom.app (Opposite.unop X)).op ≫ (shiftFunctorOpIso C 0 0 ⋯).inv.app X",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"CategoryThe... | [] | rw [← cancel_epi ((shiftFunctorZero Cᵒᵖ ℤ).hom.app X), Iso.hom_inv_id_app,
shiftFunctorZero_op_hom_app, assoc, ← op_comp_assoc, Iso.hom_inv_id_app, op_id,
id_comp, Iso.hom_inv_id_app] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Triangulated.Opposite.Basic | {
"line": 93,
"column": 2
} | {
"line": 95,
"column": 32
} | {
"line": 97,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasShift C ℤ\nX : Cᵒᵖ\n⊢ (shiftFunctorZero Cᵒᵖ ℤ).inv.app X =\n ((shiftFunctorZero C ℤ).hom.app (Opposite.unop X)).op ≫ (shiftFunctorOpIso C 0 0 ⋯).inv.app X",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
"CategoryThe... | [] | rw [← cancel_epi ((shiftFunctorZero Cᵒᵖ ℤ).hom.app X), Iso.hom_inv_id_app,
shiftFunctorZero_op_hom_app, assoc, ← op_comp_assoc, Iso.hom_inv_id_app, op_id,
id_comp, Iso.hom_inv_id_app] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 13
} | {
"line": 224,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nX : C\n⊢ adj.u... | [
"C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nX : C\n⊢ adj.unit.app ((sh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 237,
"column": 2
} | {
"line": 237,
"column": 13
} | {
"line": 237,
"column": 14
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nY : D\n⊢ (Func... | [
"C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nY : D\n⊢ (Functor.commShif... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 258,
"column": 4
} | {
"line": 258,
"column": 51
} | {
"line": 258,
"column": 52
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift C A\ninst✝² : HasShift D A\ninst✝¹ : F.CommShift A\ninst✝ : G.CommShift A\nx✝¹ : NatTrans.CommShift adj.unit A\na : A\nx✝ ... | [
"C : Type u_1\nD : Type u_2\ninst✝⁶ : Category.{v_1, u_1} C\ninst✝⁵ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁴ : AddMonoid A\ninst✝³ : HasShift C A\ninst✝² : HasShift D A\ninst✝¹ : F.CommShift A\ninst✝ : G.CommShift A\nx✝¹ : NatTrans.CommShift adj.unit A\na : A\nx✝ : D\nX : C\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 49
} | {
"line": 293,
"column": 50
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nX : C\n⊢ (shif... | [
"C : Type u_1\nD : Type u_2\ninst✝⁷ : Category.{v_1, u_1} C\ninst✝⁶ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝⁵ : AddMonoid A\ninst✝⁴ : HasShift C A\ninst✝³ : HasShift D A\ninst✝² : F.CommShift A\ninst✝¹ : G.CommShift A\ninst✝ : adj.CommShift A\na : A\nX : C\n⊢ (shiftFunctor C a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 445,
"column": 50
} | {
"line": 445,
"column": 85
} | {
"line": 445,
"column": 85
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nX : C\n⊢ b + a = 0",
"ppTerm": "?m.251",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 445,
"column": 50
} | {
"line": 445,
"column": 85
} | {
"line": 445,
"column": 85
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nX : C\n⊢ b + a = 0",
"ppTerm": "?m.251",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 445,
"column": 50
} | {
"line": 445,
"column": 85
} | {
"line": 445,
"column": 85
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nX : C\n⊢ b + a = 0",
"ppTerm": "?m.251",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 456,
"column": 43
} | {
"line": 456,
"column": 78
} | {
"line": 456,
"column": 78
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nY : C\n⊢ b + a = 0",
"ppTerm": "?m.271",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 456,
"column": 43
} | {
"line": 456,
"column": 78
} | {
"line": 456,
"column": 78
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nY : C\n⊢ b + a = 0",
"ppTerm": "?m.271",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Shift.Adjunction | {
"line": 456,
"column": 43
} | {
"line": 456,
"column": 78
} | {
"line": 456,
"column": 78
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁵ : Category.{v_1, u_1} C\ninst✝⁴ : Category.{v_2, u_2} D\nF : C ⥤ D\nG : D ⥤ C\nadj : F ⊣ G\nA : Type u_3\ninst✝³ : AddGroup A\ninst✝² : HasShift C A\ninst✝¹ : HasShift D A\na b : A\nh : a + b = 0\ninst✝ : G.CommShift A\nY : C\n⊢ b + a = 0",
"ppTerm": "?m.271",
... | [] | simp [eq_neg_of_add_eq_zero_left h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Shift.ShiftedHomOpposite | {
"line": 52,
"column": 50
} | {
"line": 56,
"column": 37
} | {
"line": 58,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : HasShift C ℤ\nX Y : C\na : ℤ\nf : ShiftedHom (Opposite.op X) (Opposite.op Y) a\nb : ℤ\nZ : C\nz : ShiftedHom X Z b\nc : ℤ\nh : b + a = c\n⊢ ((opEquiv a).symm f).comp z h = (opEquiv a).symm (Quiver.Hom.op z ≫ f) ≫ (shiftFunctorAdd' C b a c h).inv.app... | [] | by
rw [ShiftedHom.opEquiv_symm_apply, ShiftedHom.opEquiv_symm_apply,
ShiftedHom.comp]
dsimp
simp only [assoc, Functor.map_comp] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Triangulated.Yoneda | {
"line": 86,
"column": 40
} | {
"line": 88,
"column": 65
} | {
"line": 90,
"column": 0
} | [
{
"pp": "C : Type u_1\ninst✝³ : Category.{v_1, u_1} C\ninst✝² : Preadditive C\ninst✝¹ : HasShift C ℤ\ninst✝ : ∀ (n : ℤ), (shiftFunctor C n).Additive\nB : C\nn m a a' a'' : ℤ\nha' : n + a = a'\nha'' : m + a' = a''\n⊢ NatIso.ofComponents\n (fun A ↦\n (let __Equiv := Quiver.Hom.opEquiv.trans (ShiftedHo... | [] | by
ext _ x
exact ShiftedHom.opEquiv'_add_symm n m a a' a'' ha' ha'' x.op | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.SesquilinearForm.Orthogonal | {
"line": 90,
"column": 18
} | {
"line": 90,
"column": 29
} | {
"line": 90,
"column": 30
} | [
{
"pp": "K : Type u_7\nK₁ : Type u_8\nV₁ : Type u_10\nV₂ : Type u_11\ninst✝⁵ : Field K\ninst✝⁴ : Field K₁\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K₁ V₁\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nJ₁ J₁' : K₁ →+* K\nB : V₁ →ₛₗ[J₁] V₁ →ₛₗ[J₁'] V₂\nx : V₁\nhx : (B x) x ≠ 0\nμ : V₁ → K₁\nh : J₁' (μ x) • (B x... | [
"K : Type u_7\nK₁ : Type u_8\nV₁ : Type u_10\nV₂ : Type u_11\ninst✝⁵ : Field K\ninst✝⁴ : Field K₁\ninst✝³ : AddCommGroup V₁\ninst✝² : Module K₁ V₁\ninst✝¹ : AddCommGroup V₂\ninst✝ : Module K V₂\nJ₁ J₁' : K₁ →+* K\nB : V₁ →ₛₗ[J₁] V₁ →ₛₗ[J₁'] V₂\nx : V₁\nhx : (B x) x ≠ 0\nμ : V₁ → K₁\nh : J₁' (μ x) • (B x) x = 0\ny :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.SesquilinearForm.Orthogonal | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 58
} | {
"line": 131,
"column": 2
} | [
{
"pp": "R : Type u_1\nM : Type u_4\nM₁ : Type u_5\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M₁\ninst✝ : Module R M₁\nB : M →ₗ[R] M →ₗ[R] M₁\nhB : B.IsRefl\nW : Submodule R M\nhW : Disjoint W (Submodule.orthogonalBilin B W)\n⊢ (B.domRestrict₁₂ W W).Nondegenerate",... | [
"R : Type u_1\nM : Type u_4\nM₁ : Type u_5\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : AddCommGroup M₁\ninst✝ : Module R M₁\nB : M →ₗ[R] M →ₗ[R] M₁\nhB : B.IsRefl\nW : Submodule R M\nhW : Disjoint W (Submodule.orthogonalBilin B W)\n⊢ (B.domRestrict₁₂ W W).SeparatingLeft"
] | rw [(hB.domRestrict W).nondegenerate_iff_separatingLeft] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 31
} | {
"line": 170,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nL M N : C\nf : M ⟶ N\nhf : Mono f\ng : L ⟶ M\nhx : addEquiv₀.symm g ∈ ((mk₀ f).postcomp L ⋯).ker\n⊢ addEquiv₀.symm g = 0",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"CategoryTheory.Abelian.toPr... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Abelian C\ninst✝ : HasExt C\nL M N : C\nf : M ⟶ N\nhf : Mono f\ng : L ⟶ M\nhx : addEquiv₀.symm g ∈ ((mk₀ f).postcomp L ⋯).ker\n⊢ g ≫ f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Presentation.Basic | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 15
} | {
"line": 240,
"column": 16
} | [
{
"pp": "A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nπ : (relations.G →₀ A) →ₗ[A] M\nhπ : π ∘ₗ relations.map = 0\nr : relations.R\n⊢ π (relations.relation r) = 0",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
"usedF... | [
"A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nπ : (relations.G →₀ A) →ₗ[A] M\nhπ : π ∘ₗ relations.map = 0\nr : relations.R\n⊢ π (relations.relation r) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Presentation.Basic | {
"line": 263,
"column": 6
} | {
"line": 263,
"column": 67
} | {
"line": 263,
"column": 68
} | [
{
"pp": "A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.π.ker = Submodule.span A (Set.range relations.relation)\nx : relations.G →₀ A\nhx : relations.toQuotient x ∈ solution.fromQuotient.ker\n⊢ x ∈ solu... | [
"A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.π.ker = Submodule.span A (Set.range relations.relation)\nx : relations.G →₀ A\nhx : relations.toQuotient x ∈ solution.fromQuotient.ker\n⊢ solution.π x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Presentation.Basic | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 63
} | {
"line": 307,
"column": 64
} | [
{
"pp": "A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\n⊢ Function.Surjective ⇑solution.π",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Sem... | [
"A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\n⊢ Function.Surjective ⇑solution.fromQuotient"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Presentation.Basic | {
"line": 310,
"column": 2
} | {
"line": 310,
"column": 63
} | {
"line": 310,
"column": 64
} | [
{
"pp": "A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\n⊢ solution.π.ker = Submodule.span A (Set.range relations.relation)",
"ppTerm": "?m.40",
"assigned": true,
"usedConstan... | [
"A : Type u\ninst✝² : Ring A\nrelations : Relations A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\n⊢ Function.Injective ⇑solution.fromQuotient"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.Presentation.Basic | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 13
} | {
"line": 349,
"column": 14
} | [
{
"pp": "A : Type u\ninst✝⁴ : Ring A\nrelations : Relations A\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\nN : Type v'\ninst✝¹ : AddCommGroup N\ninst✝ : Module A N\nf f' : M →ₗ[A] N\nh' : solution.postcomp f = solution.postcomp f'\ng : ... | [
"A : Type u\ninst✝⁴ : Ring A\nrelations : Relations A\nM : Type v\ninst✝³ : AddCommGroup M\ninst✝² : Module A M\nsolution : relations.Solution M\nh : solution.IsPresentation\nN : Type v'\ninst✝¹ : AddCommGroup N\ninst✝ : Module A N\nf f' : M →ₗ[A] N\nh' : solution.postcomp f = solution.postcomp f'\ng : relations.G\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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